Invariance and efficiency of convex representations
We consider two notions for the representations of convex cones: G-representation and lifted-G-representation. The former represents a convex cone as a slice of another; the latter allows in addition, the usage of auxiliary variables in the representation.We first study the basic properties of these...
| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
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2009
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| Online Access: | https://hdl.handle.net/10356/91764 http://hdl.handle.net/10220/4712 |
| _version_ | 1811686665249357824 |
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| author | Chua, Chek Beng. Tunçel, Levent. |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Chua, Chek Beng. Tunçel, Levent. |
| author_sort | Chua, Chek Beng. |
| collection | NTU |
| description | We consider two notions for the representations of convex cones: G-representation and lifted-G-representation. The former represents a convex cone as a slice of another; the latter allows in addition, the usage of auxiliary variables in the representation.We first study the basic properties of these representations. We show that some basic properties of convex cones are invariant under one notion of representation but not the other. In particular, we prove that lifted-G-representation is closed under duality when the representing cone is self-dual.We also prove that strict mplementarity of a convex optimization problem in conic form is preserved under G-representations. Then we move to study efficiency measures for representations.We evaluate the representations of homogeneous convex cones based on the “smoothness” of the transformations mapping the central path of the representation to the central path of the represented optimization problem. |
| first_indexed | 2024-10-01T05:04:02Z |
| format | Journal Article |
| id | ntu-10356/91764 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:04:02Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | ntu-10356/917642023-02-28T19:29:53Z Invariance and efficiency of convex representations Chua, Chek Beng. Tunçel, Levent. School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Applied mathematics::Optimization We consider two notions for the representations of convex cones: G-representation and lifted-G-representation. The former represents a convex cone as a slice of another; the latter allows in addition, the usage of auxiliary variables in the representation.We first study the basic properties of these representations. We show that some basic properties of convex cones are invariant under one notion of representation but not the other. In particular, we prove that lifted-G-representation is closed under duality when the representing cone is self-dual.We also prove that strict mplementarity of a convex optimization problem in conic form is preserved under G-representations. Then we move to study efficiency measures for representations.We evaluate the representations of homogeneous convex cones based on the “smoothness” of the transformations mapping the central path of the representation to the central path of the represented optimization problem. Accepted version 2009-07-28T06:27:56Z 2019-12-06T18:11:35Z 2009-07-28T06:27:56Z 2019-12-06T18:11:35Z 2006 2006 Journal Article Chua, C. B., & Tunçel, L. (2006). Invariance and efficiency of convex representations. Mathematical Programming, 113-140. 0025-5610 https://hdl.handle.net/10356/91764 http://hdl.handle.net/10220/4712 10.1007/s10107-006-0072-6 en Mathematical programming Mathematical Programming @ copyright 2006 Springer-Verlag. The journal's website is located at http://www.springerlink.com.ezlibproxy1.ntu.edu.sg/content/103081. 25 p. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics::Applied mathematics::Optimization Chua, Chek Beng. Tunçel, Levent. Invariance and efficiency of convex representations |
| title | Invariance and efficiency of convex representations |
| title_full | Invariance and efficiency of convex representations |
| title_fullStr | Invariance and efficiency of convex representations |
| title_full_unstemmed | Invariance and efficiency of convex representations |
| title_short | Invariance and efficiency of convex representations |
| title_sort | invariance and efficiency of convex representations |
| topic | DRNTU::Science::Mathematics::Applied mathematics::Optimization |
| url | https://hdl.handle.net/10356/91764 http://hdl.handle.net/10220/4712 |
| work_keys_str_mv | AT chuachekbeng invarianceandefficiencyofconvexrepresentations AT tuncellevent invarianceandefficiencyofconvexrepresentations |